Scilab Function
Last update : Dec 1997

cdfchn - cumulative distribution function non-central chi-square distribution

### Calling Sequence

  `[P,Q]=cdfchn("PQ",X,Df,Pnonc)`
  `[X]=cdfchn("X",Df,Pnonc,P,Q);`
  `[Df]=cdfchn("Df",Pnonc,P,Q,X)`
  `[Pnonc]=cdfchn("Pnonc",P,Q,X,Df)`

### Parameters

- `P,Q,X,Df,Pnonc`: five real vectors of the same size.
- `P,Q (Q=1-P)` : The integral from 0 to X of the non-central chi-square distribution. Input range: [0, 1-1E-16).
- `X`: Upper limit of integration of the non-central chi-square distribution. Input range: [0, +infinity). Search range: [0,1E300]
- `Df`: Degrees of freedom of the non-central chi-square distribution. Input range: (0, +infinity). Search range: [ 1E-300, 1E300]
- `Pnonc`: Non-centrality parameter of the non-central chi-square distribution. Input range: [0, +infinity). Search range: [0,1E4]

### Description

Calculates any one parameter of the non-central chi-square distribution given values for the others.

Formula 26.4.25 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to compute the cumulative distribution function.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

The computation time required for this routine is proportional to the noncentrality parameter (PNONC). Very large values of this parameter can consume immense computer resources. This is why the search range is bounded by 10,000.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.